Sigma Notation and area under curve

[Tueseve728]

By following the steps below, find the exact area under the curve y=f(x)=x^2+2 from x=0 to x=2. Use the upper sum approximation.
Step 1: Divide the interval into n pieces, be sure to write down the k^th piece.

Step 2: Write the finite approximation Sn=A1+A2+......+Ak+....+An (the n1,2,k and are subscripts)

Step 3: Find the exact area under the curve y=f(x) by taking the limit as n approaches infinity of the expression in Step 2.

 

[jsbeckton]

Did you try it? You have to see the patterns to find the sumation equation.

\(\displaystyle \begin{array}{l}
{\rm The first one would look like x= }\sum\limits_{i = 1}^{50} {\frac{1}{{2i}}} \\
{\rm It is a sum of }\frac{{\rm 1}}{{{\rm 2i}}}{\rm as i ranges from 1 to 50} \\
\end{array}\)